(7x-2)(11x-34)=18

Solution for (7x-2)(11x-34)=18 equation:

(7x-2)(11x-34)=18

We move all terms to the left:

(7x-2)(11x-34)-(18)=0

We multiply parentheses ..

(+77x^2-238x-22x+68)-18=0

We get rid of parentheses

77x^2-238x-22x+68-18=0

We add all the numbers together, and all the variables

77x^2-260x+50=0

a = 77; b = -260; c = +50;
Δ = b2-4ac
Δ = -2602-4·77·50
Δ = 52200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52200}=\sqrt{900*58}=\sqrt{900}*\sqrt{58}=30\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-260)-30\sqrt{58}}{2*77}=\frac{260-30\sqrt{58}}{154}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-260)+30\sqrt{58}}{2*77}=\frac{260+30\sqrt{58}}{154}
$